Use synthetic division to solve (4x^3-3x^2+5x+6) divided by (x+6) What is the quotient?

As x+6 is the quotient, you need to use - 6

-6 | 4 - 3 + 5 6

x - 24 + 162 - 1002

add

4 - 27 167 - 996

f (x) = 4x^2 - 27x + 167 - 996 / (x+6)

Lets check

(x+6) (4x^2 - 27x + 167) = 4x^3 - 27x^2 + 167x + 24x^2 - 162x + 1002 =

= 4x^3 - 3x^2 + 5x + 1002

1002-996 = 6

So we have the correct solution: 4x^2 - 27x + 167 - 996 / (x+6)